Public learning track
Applications of Derivatives: Tangents, Extrema, and Curve Sketching
11th Grade · Math · Open Global Math
8 lessons
Goal
Construct tangent and normal lines, classify local and global extrema, and sketch complex transcendental curves.
Featured Diagrams
Finding Equations of Tangents to Curves
8 lessons
0 of 8 done
- 1Finding Equations of Tangents to CurvesUp nextStart
- 2Finding Equations of Normals to CurvesPremiumNot started yet
- 3Intervals of Increase, Decrease, and Local ExtremaNot started yet
- 4Locating Stationary Points on Polynomial and Rational CurvesNot started yet
- 5Locating Stationary Points on Exponential and Trigonometric CurvesNot started yet
- 6Global Extrema on Closed and Bounded IntervalsNot started yet
- 7Curve Sketching with Exponential, Logarithmic, and Trigonometric FunctionsNot started yet
- 8Applied Optimization in Geometry and EconomicsNot started yet
Standards Covered
- OGM.12.CAL.3Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Apply differentiation to find equations of tangents and normals, identify intervals of increase/decrease, locate and classify stationary points (local/global extrema, points of inflection), and differentiate implicitly and parametrically.
- OGM.12.CAL.1Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Understand the derivative f'(x) as the limit of the difference quotient and as the gradient of the tangent; differentiate x^n, sin(x), cos(x) from first principles; compute second derivatives to determine convexity, concavity, and points of inflection.
Curriculum Framework
11th Grade · Math · Open Global Math
1
7 lessons
First Principles and Foundations of Derivatives
Derive the derivative definition from difference quotients, prove standard derivatives from first principles, and analyze second derivatives and curvature.
2
11 lessons
Advanced Differentiation Rules and Transcendental Functions
Differentiate exponential, logarithmic, and trigonometric functions using chain, product, and quotient rules.
3
7 lessons
Implicit and Parametric Differentiation and Rates of Change
Differentiate implicit equations and parametric curves, and solve connected rates of change modeling problems.
4
8 lessons
Applications of Derivatives: Tangents, Extrema, and Curve Sketching
Construct tangent and normal lines, classify local and global extrema, and sketch complex transcendental curves.
5
8 lessons
Definite Integrals, Riemann Sums, and the Fundamental Theorem of Calculus
Interpret definite integrals as limits of Riemann sums, apply the Fundamental Theorem of Calculus, and calculate areas under and between curves.
6
9 lessons
Advanced Integration Techniques: Substitution, Parts, and Partial Fractions
Evaluate non-standard integrals using algebraic substitution, integration by parts, and partial fraction decompositions.
7
6 lessons
First-Order Differential Equations and Modeling
Formulate, solve, and interpret separable first-order differential equations in physical, biological, and kinematic contexts.
8
7 lessons
Numerical Calculus and Iterative Methods
Locate roots via sign change, solve equations using fixed-point iteration and Newton-Raphson, and approximate integrals with the trapezium rule.